Finally, we compare the proposed CTAD algorithm and the URA schemes designed in [1]} and [2]}. In Fig. REF , we consider a scenario that the direct channel link between the BS and devices is not completely blocked such that a weak signal can reach the BS through the direct link. It is assumed that the direct channel link obeys an i.i.d. Gaussian distribution with zero mean and \(0.3\)  variance.
Without the aid of RIS, the URA schemes designed in [1]} and [2]} perform active device detection only with weak direct link signals. Accordingly, the proposed CTAD algorithm performs active device separation only based on IRS-associated signals. It can be seen that the PER performance of the proposed algorithm is significantly better than that of URA schemes designed in [1]} and [2]}. There are two main reasons, the first is that the proposed algorithm exploits the prior statistical distributions of the sparse channel, which is ignored by the algorithms in [1]} and [2]}. On the other hand, the RIS can reflect impinging
electromagnetic waves with a controllable phase shift via the
help of a smart controller. Through the passive beamforming designed in Section III-A, the RIS is able to provide an extra high-quality channel link to overcome the unfavourable propagation conditions of URA systems.
